Now we are ready to present the thresholds of our hybrid architecture.
Our first result is the error threshold of the RHG-GKP code with approximate GKP states, which we model as ideal states suffering a random displacement with noise variance \(\delta \) , as discussed in subsec:noise.
In our noise model, this corresponds to the limit of no swap-outs, i.e., \(p_0 = 0\) .
Similar simulations have been carried out in previous works for the toric-GKP code [1]} and the surface-GKP code [2]}, [3]}. We use standard binning and matching graph weights derived from eq:errorprob.
We observe an error threshold of \(\Delta _{\rm dB} = -10\log _{10}(\delta ) \approx 10.5~\rm dB\) , which is comparable with results for similar noise models in the aforementioned works.
The data are shown in fig:raussendorf-gkp.
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